Most object based graphics systems utilise a frame store or page buffer to hold a pixel-based image of the page or screen. Typically, the outlines of the graphic objects are calculated, filled and written into the frame store. For two-dimensional graphics, objects which appear in front of other objects are simply written into the frame store after the background objects, thereby replacing the background on a pixel-by-pixel basis. This is commonly known in the art as the “Painter's algorithm”. Objects are considered in priority order, from the rearmost object to the foremost object, and, typically, each object is rasterised in scan line order and pixels are written to the frame store in sequential runs along each scan line.
There are essentially two problems with this technique. The first is that it requires fast random access to all the pixels in the frame store. This is because each new object considered could affect any pixel in the frame-store. For this reason, the frame store is normally kept in semiconductor random access memory (RAM). For high resolution colour printers the amount of RAM required is very large, typically in excess of 100 MBytes, which is costly and difficult to operate at high speed. The second problem is that many pixels, which are painted (rendered), are over-painted (re-rendered) by later objects. Painting the pixels with the earlier objects was a waste of time.
One method for overcoming the large frame-store problem is the use of “banding”. When banding is used, only part of the frame-store exists in memory at any one time. All of the objects to be drawn are retained in a “display list”. The whole image is rendered as above, but pixel painting (rendering) operations that try to paint (render) outside the fraction of the frame-store which exists are “clipped” out. After all the objects have been drawn, the fractional part of the frame-store is sent to the printer (or some other location) and another fraction of the frame-store is selected and the process repeated. There are penalties with this technique. For example, the objects being drawn must be considered and re-considered many times—once for each band. As the number of bands increases, so too does the repetitious examination of objects requiring rendering. The technique of banding does not solve the problem of the cost of over-painting.
Some other graphic systems consider the image in scan line order. Again, all the objects to be drawn are retained in a display list. On each scan line the objects which intersect that scan line are then considered in priority order and for each object, spans of pixels between object edge intersection points are set in a line store. This technique also overcomes the large frame store problem, but still suffers from the over-paint problem.
There are other techniques, which overcome both the large frame-store problem and the over-painting problem. In one such technique, each scan line is produced in turn. Again, all the objects to be drawn are retained in a display list. On each scan line, the edges of objects which intersect that scan line are held in order of increasing coordinate of intersection with the scan line. These points of intersection, or edge crossings, are considered in turn and used to toggle an array of active fields. There is one active field for each object priority that is of interest on the scan line. Between each pair of edges considered, the colour data for each pixel which lies between the first edge and the next edge is generated by using a priority encoder on the active flags to determine which priority is topmost, and using the colour associated with that priority for the pixels of the span between the two edges. In preparation for the next scan line, the coordinate of intersection of each edge is updated in accordance with the nature of each edge. Adjacent edges, which become mis-sorted as a result of this update are swapped. New edges are also merged into the list of edges.
This technique has the significant advantages that there is no frame store or line store, there is no over painting, and the object priorities are dealt with in constant order time, rather than order N time (where N is the number of priorities).
However, these priority encoders lack sufficient flexibility to cope with a tree based graphical expression. In particular, those expressions which include OUT and ATOP Porter and Duff compositing operators as described in “Compositing Digital Images”, Porter, T; Duff, T; Computer Graphics, Vol. 18 No. 3 (1984) pp. 253-259. The problems arise because the compositing operation depends on which of the graphic objects composited by the operation are active at a given pixel location. One solution to this problem is to use a complex arrangement of clipping objects, which requires a lot of extra edge processing and requires a large number of levels for the clipping objects.